%%%%%%%%% \section{Table - Insurer Operating Results By Portfolio Size}
%%%%%%%%% \label{tab:InsurerOperatingResultsByPortfolioSize}
%\vspace{-1in}
\begin{table}[htbp]
%\vspace{-1in}
\caption{Reinsurance Pricing And Risk Loading By Portfolio Size} 
\begin{center}
\scalebox{0.75}{
\begin{tabular}{rrcrrrrrr}
%\multicolumn{2}{c}{Genotype} & &
%\multicolumn{1}{c}{Dummy for additivity} &
%\multicolumn{1}{c}{Dummy for dominance }\\
%\multicolumn{1}{c}{Label} &    
%\multicolumn{1}{c}{Index i} &
%\multicolumn{1}{c}{Genotypic value ($\eta$)}&
%\multicolumn{1}{c}{effect $\alpha$ (x)} &
%\multicolumn{1}{c}{effect $\delta$ (z)}\\
\hline
\hline
	&	&	&	\multicolumn{1}{c}{Risk}	&	&	\multicolumn{1}{c}{Risk}	&	& \multicolumn{1}{c}{Risk}	& \\

	&	&	&	\multicolumn{1}{c}{Loaded}	&	&	\multicolumn{1}{c}{Loaded}	&	& \multicolumn{1}{c}{Loaded}	& \\

	&		&		&	\multicolumn{1}{c}{Reinsurance}	& &	\multicolumn{1}{c}{Reinsurance}	&	&	\multicolumn{1}{c}{Reinsurance}	&		\\

	&		&		&	\multicolumn{1}{c}{(Capitation)}	&	& \multicolumn{1}{c}{(Capitation)} &	&	\multicolumn{1}{c}{(Capitation)}	&		\\
\multicolumn{1}{c}{Portfolio}	&		&	\multicolumn{1}{c}{Standard}	&	\multicolumn{1}{c}{Payment} & \multicolumn{1}{c}{PI's}	&	\multicolumn{1}{c}{Payment}	&	\multicolumn{1}{c}{PI's}	&	\multicolumn{1}{c}{Payment}	&	\multicolumn{1}{c}{PI's}	\\
\multicolumn{1}{c}{Size}	&	\multicolumn{1}{c}{Premiums}	&	\multicolumn{1}{c}{Error}	&	\multicolumn{1}{c}{Profits $\geq$ 5\%}	&	\multicolumn{1}{c}{Profits}	&	\multicolumn{1}{c}{Profits $\geq$ 0\%}	&	\multicolumn{1}{c}{Profits}	&	\multicolumn{1}{c}{Losses $\leq$ 10\%}	&	\multicolumn{1}{c}{Profits}	\\
\hline
309,000,000	&	\$1,236,000,000,000	&	0.002844	&	0.8028	&	4.72	&	0.7557	&	9.43	&	0.7585	&	9.15	\\
300,000,000	&	\$1,200,000,000,000	&	0.002887	&	0.8029	&	4.71	&	0.7558	&	9.42	&	0.7587	&	9.13	\\
250,000,000	&	\$1,000,000,000,000	&	0.003162	&	0.8032	&	4.68	&	0.7563	&	9.37	&	0.7595	&	9.05	\\
200,000,000	&	\$800,000,000,000	&	0.003536	&	0.8035	&	4.65	&	0.7571	&	9.29	&	0.7606	&	8.94	\\
150,000,000	&	\$600,000,000,000	&	0.004082	&	0.8041	&	4.59	&	0.7582	&	9.18	&	0.7622	&	8.78	\\
100,000,000	&	\$400,000,000,000	&	0.005000	&	0.8050	&	4.50	&	0.7600	&	9.00	&	0.7650	&	8.50	\\
50,000,000	&	\$200,000,000,000	&	0.007071	&	0.8071	&	4.29	&	0.7641	&	8.59	&	0.7712	&	7.88	\\
40,000,000	&	\$160,000,000,000	&	0.007906	&	0.8079	&	4.21	&	0.7658	&	8.42	&	0.7737	&	7.63	\\
30,000,000	&	\$120,000,000,000	&	0.009129	&	0.8091	&	4.09	&	0.7683	&	8.17	&	0.7774	&	7.26	\\
20,000,000	&	\$80,000,000,000	&	0.011180	&	0.8112	&	3.88	&	0.7724	&	7.76	&	0.7835	&	6.65	\\
10,000,000	&	\$40,000,000,000	&	0.015811	&	0.8158	&	3.42	&	0.7816	&	6.84	&	0.7974	&	5.26	\\
1,000,000	&	\$4,000,000,000	&	0.050000	&	0.8500	&	0.00	&	0.8500	&	0.00	&	0.9000	&	-5.00	\\
900,000	&	\$3,600,000,000	&	0.052705	&	0.8527	&	-0.27	&	0.8554	&	-0.54	&	0.9081	&	-5.81	\\
800,000	&	\$3,200,000,000	&	0.055902	&	0.8559	&	-0.59	&	0.8618	&	-1.18	&	0.9177	&	-6.77	\\
700,000	&	\$2,800,000,000	&	0.059761	&	0.8598	&	-0.98	&	0.8695	&	-1.95	&	0.9293	&	-7.93	\\
600,000	&	\$2,400,000,000	&	0.064550	&	0.8645	&	-1.45	&	0.8791	&	-2.91	&	0.9436	&	-9.36	\\
500,000	&	\$2,000,000,000	&	0.070711	&	0.8707	&	-2.07	&	0.8914	&	-4.14	&	0.9621	&	-11.21	\\
400,000	&	\$1,600,000,000	&	0.079057	&	0.8791	&	-2.91	&	0.9081	&	-5.81	&	0.9872	&	-13.72	\\
300,000	&	\$1,200,000,000	&	0.091287	&	0.8913	&	-4.13	&	0.9326	&	-8.26	&	1.0239	&	-17.39	\\
200,000	&	\$800,000,000	&	0.111803	&	0.9118	&	-6.18	&	0.9736	&	-12.36	&	1.0854	&	-23.54	\\
100,000	&	\$400,000,000	&	0.158114	&	0.9581	&	-10.81	&	1.0662	&	-21.62	&	1.2243	&	-37.43	\\
90,000	&	\$360,000,000	&	0.166667	&	0.9667	&	-11.67	&	1.0833	&	-23.33	&	1.2500	&	-40.00	\\
80,000	&	\$320,000,000	&	0.176777	&	0.9768	&	-12.68	&	1.1036	&	-25.36	&	1.2803	&	-43.03	\\
70,000	&	\$280,000,000	&	0.188982	&	0.9890	&	-13.90	&	1.1280	&	-27.80	&	1.3169	&	-46.69	\\
60,000	&	\$240,000,000	&	0.204124	&	1.0041	&	-15.41	&	1.1582	&	-30.82	&	1.3624	&	-51.24	\\
50,000	&	\$200,000,000	&	0.223607	&	1.0236	&	-17.36	&	1.1972	&	-34.72	&	1.4208	&	-57.08	\\
40,000	&	\$160,000,000	&	0.250000	&	1.0500	&	-20.00	&	1.2500	&	-40.00	&	1.5000	&	-65.00	\\
30,000	&	\$120,000,000	&	0.288675	&	1.0887	&	-23.87	&	1.3274	&	-47.74	&	1.6160	&	-76.60	\\
20,000	&	\$80,000,000	&	0.353553	&	1.1536	&	-30.36	&	1.4571	&	-60.71	&	1.8107	&	-96.07	\\
10,000	&	\$40,000,000	&	0.500000	&	1.3000	&	-45.00	&	1.7500	&	-90.00	&	2.2500	&	-140.00	\\
5,000	&	\$20,000,000	&	0.707107	&	1.5071	&	-65.71	&	2.1642	&	-131.42	&	2.8713	&	-202.13	\\
1,000	&	\$4,000,000	&	1.581139	&	2.3811	&	-153.11	&	3.9123	&	-306.23	&	5.4934	&	-464.34	\\
100	&	\$400,000	&	5.000000	&	5.8000	&	-495.00	&	10.7500	&	-990.00	&	15.7500	&	-1,490.00	\\
10	&	\$40,000	&	15.811388	&	16.6114	&	-1,576.14 & 32.3728 & -3,152.28	& 48.1842 &	-4,733.42	\\
1	&	\$4,000	&	50.000000	&	50.8000	&	-4,995.00	& 100.7500 & -9,990.00	& 150.7500 & -14,990.00	\\
\hline
\end{tabular}\label{tab:RiskLoadedReinsurancePremiumsByPortfolioSize}
}
\end{center}
Notes: \\
Match Prob[PI's Profits $\geq$ 5\%] = 0.8413: Risk Loaded Payment = 0.7500 + 1 * $\sigma_{e_{N}}$ \\
Match Prob[PI's Profits $\geq$ 0\%] = 0.9772: Risk Loaded Payment = 0.7500 + 2 * $\sigma_{e_{N}}$ \\
Match Prob[PI's Losses $\leq$ 5\%] = 0.9987: Risk Loaded Payment = 0.7500 + 3 * $\sigma_{e_{N}}$ \\
\end{table}

